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The requests, which will be sent to the council, were resolutions from a public meeting of local residents on Saturday afternoon organised by Dunedin South MP Clare Curran.
More than 30 people attended the meeting, held at David and Kerry Hiom's home. People expressed fear the lower hump of Saddle Hill, Jaffray Hill, was in danger of collapse if quarrying continued.
The group also wanted an urgent independent stability analysis, a mine safety inspection, and called for the council to investigate public ownership of the disputed quarry.
The meeting came as the council decides whether to appeal a High Court decision last month that consent did exist for the disputed quarry, overturning an Environment Court ruling.
A decision is expected on Wednesday. The High Court also recommended the council and quarry owner Saddle Views Estate Ltd (SVE) work together to settle the terms of the consent and mediation on that will start if the council does not appeal.
SVE sole director Calvin Fisher, an official from the Amalgamated Workers Union, which owns SVE, said suggestions the hill was in danger of collapsing were ''ridiculous''.
''It's not in our interest to be quarrying in such a way that that would occur,'' Mr Fisher said.
It was clear the council had an agenda to stop quarrying even though it originally told ratepayers it was going to court to get an opinion on its legality, he said.
At the meeting, it was agreed Ms Curran would request a meeting with Edward Ellison, of Ngai Tahu, to garner his view, and with Amalgamated Workers Union, which owns the quarry company. Ms Curran said Mr Ellison expressed ''deep concern'' to her when contacted about the situation.
The meeting was attended by local community board chairmen Scott Weatherall and Bill Feather, Dunedin city councillor Andrew Whiley and former councillor Colin Weatherall. DCC staff sent apologies as they were unable to attend due to legal considerations.
Economic considerations, such as the need for cheap material for roads, should be acknowledged but had to be put to one side, Ms Curran said.
''I do think there is a sense of real urgency here, because this hill could collapse.
''And if it collapses, then we've lost the hill, we've lost the landmark.''
After the meeting, Ms Curran said she had received multiple reports of a rock fall on Jaffray Hill.
Some people expressed concern about the council buying metal from the quarry at the same time as challenging its existence.
Cr Whiley said the quarry owner should hold an open day for the community to see the work, and allow the public to judge whether it was being conducted properly.
Neville Jemmett, of Saddle Hill, told Cr Whiley there was no point in holding an open day. ''Even if they're doing [the quarrying] correctly ... that skyline is changing, irrespective of whether they're doing it right or wrong, it is changing shape all the time.
''The top's coming off it.''
Ms Curran was asked if she had a conflict of interest, because the quarry was owned by a union, and she was a Labour politician.
Rejecting that, she said the Amalgamated Workers Union was not affiliated with either the Labour Party or the Council of Trade Unions. She said Mr Fisher had ''nothing to do'' with the Labour Party.
Saddle Hill Community Board chairman Scott Weatherall said he was frequently asked about the quarry by concerned members of the public. He said the strong view of the community was that quarrying must stop.
David Barrell, a geologist, of Mosgiel, suggested the group request an independent stability analysis of the hill, which was adopted.